SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES

doi:10.1016/S0252-9602(16)30116-3

Abstract

Abstract:

Let A be the space of functions analytic in the unit disk D={z:|z|<1}. Let U denote the set of all functions f∈A satisfying the conditions f(0)=f'(0) 1=0 and
|f'(z)((z)/(f(z)))²-1|<1 (|z|< 1).
Also, let denote the set of all functions f∈A satisfying the conditions f(0)=f'(0)-1=0 and
|zf'(z)-f(z)|<(1)/(2) (|z|<1).
In this article, we discuss the properties of U and Ω.

Key words: univalent function, Starlike function, Hadamard product, extreme point, support point

Zhigang PENG, Gangzhen ZHONG. SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES[J].Acta mathematica scientia,Series B, 2017, 37(1): 69-78.

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